ALGEBRA II Honors
2013–2014 SEMESTER EXAMS
PRACTICE MATERIALS
SEMESTER 1
1. A student has learned that test scores in math are determined by this quadratic function:
In the function, is the score and is the number of hours that a student spends on homework each week.
a) How many hours must a student spend on homework to achieve maximum score?
b) What is the maximum score?
c) Based on the function, what will be the score if a student does no homework?
2. Show that is a root of .
3. Solve over the set of complex numbers.
(A)
(B)
(C)
(D)
4. Which of the following quadratic equation has no real roots?
(A)
(B)
(C)
(D)
5. According to the Fundamental Theorem of Algebra, how many roots does the following equation have?
(A) 2
(B) 4
(C) 6
(D) 11
6. Function A and Function B are continuous quadratic functions.
Function A Function B
Which function has a greater positive x-intercept?
(A) Function A
(B) Function B
7. What is the equation of the parabola shown?
(A)
(B)
(C)
(D)
8. Factor .
(A)
(B)
(C)
(D)
9. Solve the equation by factoring.
(A)
(B)
(C)
(D)
10. Solve the quadratic equation by taking the square root.
(A)
(B)
(C)
(D)
11. Solve the equation by using the quadratic formula.
(A)
(B)
(C)
12. Simplify.
(A)
(B)
(C)
(D)
13. Simplify.
(A)
(B)
(C)
(D)
14. Find the vertex of and state if it is a maximum or a minimum.
(A) (-1, -4); maximum
(B) (-1, -4); minimum
(C) (-4, -1); maximum
(D) (-4, -1); minimum
15. The height of Carl, the human cannonball, is given by where is in feet and is in seconds after the launch.
a) What was his height at the launch?
b) What is his maximum height?
c) How long before he lands in the safety net, 8 feet above the ground?
16. What is the solution set of?
(A)
(B)
(C)
(D)
17. Which of the following is a factor of?
(A)
(B)
(C)
(D)
18. Consider the function
a) Determine the roots of the function. Show your work.
b) The vertex of is the point (3, 30). Write the function rule for in vertex form.
c) Explain how transformed to become .
19. Several values of the quadratic function are given in the table.
The function is given by. Which function has the greater maximum for which value of?
(A)
(B)
(C)
(D)
20. Which statement best describes these two functions?
(A) The maximum of is less than the minimum of.
(B) The minimum of is less than the maximum of.
(C) The maximum of is greater than the minimum of.
(D) The minimum of is greater than the maximum of.
21. Given the general form of a quadratic equation, determine the effect of each condition on the solutions.
a)
b)
c)
d) What is needed for the solutions to have imaginary parts?
22. The amount of fuel (in billions of gallons) used by trucks from 1990 through 2009 can be approximated by the function where represents 1990.
a) Describe the transformation of the common function. Then sketch the graph over the interval
b) Find and interpret.
c) Rewrite the function so that represents 2000. Explain how you got your answer.
d) Use the model from part (c) to predict the amount of fuel used by trucks in 2015. Does your answer seem reasonable? Explain.
23. Use the graph provided to choose the best description of what the graph represents.
(A) A ball I dropped from a height of 42 feet and lands on the ground after 3 seconds.
(B) A ball is dropped from a height of 42 feet and lands on the ground after 1.5 seconds.
(C) A ball is shot up in the air and reaches a height of 42 feet after 1 second.
(D) A ball is shot up in the air, reaches a height of 42 feet, and lands on the ground after 1.5 seconds.
24. The table lists all the real roots of a 5th degree polynomial and the multiplicity of each root.
Which general factorization correctly represents?
(A)
(B)
(C)
(D)
25. A 4th degree polynomial with real coefficients is found to have exactly two distinct real roots. What must be true about the other two roots?
(A) One root is real and the other is imaginary.
(B) Both roots must be real.
(C) Both roots are imaginary roots that are complex conjugates.
(D) All the roots have been found.
26. Consider the graph of below. Which general factorization correctly represents .
Which general factorization correctly represents?
(A)
(B)
(C)
(D)
27. The graph of is shown below.
Which general factorization correctly represents?
(A)
(B)
(C)
(D)
28. Use the graph of to answer questions.
a) True or False: The leading term of, when written in standard form, is positive.
b) True or False: From the graph,. The multiplicity of the factor is even. Explain your answer.
29. If, find the possible rational roots of .
(A)
(B)
(C)
(D)
30. Given polynomial, . Which statement is correct?
(A) is not a root
(B) is a root
(C) is a factor
(D) is not a factor
31. Consider.
a) Show that and are zeros of.
b) Completely factor where all the coefficients are rational numbers.
c) istranslated 4 units right and 2 units up. What is the equation of?
32.
a) Show that is a root.
b) Factor completely
c) If, what are the real roots of?
33. Given the polynomial:
a) Show that is a root.
b) What other root must also be a root of? Explain.
c) Factor completely.
34. Consider.
a) Show that are roots of, then write as the appropriate factorizations at this point.
b) Factor completely.
c) Let. List out the roots of.
d) Letbevertically stretched by 2, translated 2 units to the right and 4 units up. Write out the algebraic relationship between and.
35. What is the 4th term of the expanded binomial?
(A)
(B)
(C)
(D)
36. For what values of will have exactly one distinct real root?
(A)
(B)
(C)
(D)
37. Write a cubic function that passes through the following points: (-2, 0) (3, 0) (-1, 0) and (1, 2).
(A)
(B)
(C)
(D)
38. How many possible rational zeros exist for the polynomial function ?
(A) 9
(B) 12
(C) 18
(D) 24
39. Suppose and. What is?
(A) 3
(B) 12
(C) 36
(D) 81
40.
Which graph represents?
(A)
(B)
(C)
(D)
41. Divide using long division.
(A)
(B)
(C)
(D)
42. This polynomial function has at least one rational root.
a) What are all the possible integer values of? Show your work or explain how you know.
b) What are all the possible real roots of the function? Show your work or explain how you know.
43. The volume and height () of the prism is given. Find a polynomial expression for the area of the base () in terms of. (Hint: )
(A)
(B)
(C)
(D)
44. Consider the function.
a) Use the leading coefficient and degree of to describe the end behavior.
b) Write the rule for the function, and describe the transformation.
c) Describe the end behavior of. How does the end behavior of relate to the transformation of?
45. Use the information in the table.
a) What are the three real zeros of the polynomial function?
b) What can be said about the behavior of the graph of at?
c) What is the least possible degree of? Explain. Can the degree of ever be even? Explain.
46. The town of Frostburg experienced a bit of a heat wave during January of this year. The graph below shows the curve of best fit that represents the low temperature of every day in January.
A newspaper journalist is writing a story on the weather and needs to report some information. He needs a bit of guidance with interpreting the graph.
1) Write a few sentences describing the key characteristics of the graphs as it relates to the context of the problem. Be sure to include domain, range, intervals where the function increases and decreases, x and y intercepts, and any other important information
46. (cont.…)
The graph below shows the curve of best fit that represents the low temperature of every day in February.
2) Three different models have been proposed that could be used to determine the temperature for a particular date in February. The models are given below:
Model 1:
Model 2:
Model 3:
Which model would best describe the low temperatures for February? Explain why you chose that model.
The weather in July showed a related pattern to the weather in February. The curve of best fit for July is shown below:
3) Explain the relationship between the graph for February and the graph for July. Use that relationship to create an equation for the temperatures in July.
47. If and , which expression represents for ?
(A)
(B)
(C)
(D)
48. Which value of makes this equation true?
(A) 1
(B) 7
(C) 8
(D) 34
49. Solve for:
(A)
(B)
(C)
(D) No real solution
50. Solve for.
(A)
(B)
(C)
(D) No real solutions
51. Solve for.
(A)
(B)
(C)
(D) No real solutions
52. Identify theand intercepts of the function .
(A) (8,0) and (0,-2)
(B) (2,0) and (0,2)
(C) (8,0) and (0,8)
(D) (-2,0) and (0,8)
53. Which is the domain of the function?
(A)
(B)
(C)
(D)
54. Compare the graph of with the graph of its parent function.
(A) Shifts 6 units down
(B) Reflects across the x-axis and shifts 6 units down
(C) Reflects across the x-axis and shifts 6 units up
(D) Reflects across the y-axis and shifts 6 units up
55. If , what is the value of ?
(A) -8
(B) 3
(C) 12
(D) 27
56. In 1950, the city of San Jose had a population of 95,000. Since then, on average, it grows 4% per year. What is the best formula to model San Jose’s growth?
(A) 95,000(1.04)t
(B) 95,000(0.96)t
(C) -.04t + 95,000
(D) .04t + 95,000
57. A biologist studying the relationship between the brain weight and body weight in mammals uses the formula:
Where =body weight in grams and=brain weight in grams. What is the formula for the body weight?
(A)
(B)
(C)
(D)
58. Find the value of.
(A) 5
(B) 1024
(C) 16
(D) 4
59. Given the sequence 1, 2, 4, 8, ….
Find the sum of the infinite series.
(A) 15
(B) 18
(C) 30
(D)
60. During a flu outbreak, a hospital recorded 12 cases the first week, 54 cases the second week, and 243 cases the third week.
a) Write a geometric sequence to model the flu outbreak.
b) How many cases will occur in the sixth week if the hospital cannot stop the outbreak?
61. Which is the same function as?
(A)
(B)
(C)
(D)
62. Rewrite in exponential form.
(A)
(B)
(C)
(D)
63. Given the geometric sequence with common ratio , write a rule for the nth term of the sequence 4, -28, 196, -1372…
(A)
(B)
(C)
(D)
64. Choose the function that describes the graph below:
(A)
(B)
(C)
(D)
65. Sarai bought $400 of Las Vegas Cellular stock in January 2005. The value of the stock is expected to increase by 6.5% per year.
a) Write a model to describe Sarai’s investment.
b) Use the graph to show when Sarai’s investment will reach $1100?
66. Consider the function.
a) Identify the transformation applied to to create.
b) Identify the transformation applied to to create.
c) Compare the graphs of and . What do you notice?
d) Use the properties of logarithms to explain your answer to part c.
67. What is the value of?
(A) -42
(B) -17
(C) 88
(D) 363
68. What function is represented by the following graph?
(A)
(B)
(C)
(D)
69. The graph of the equation is translated right 3 units and down 3.5 units to form a new graph. Which equation best represents the new graph?
(A)
(B)
(C)
(D)
70. John graphs the equation. Lana graphs the equation. How does Lana’s graph compare to John’s graph?
(A) Lana’s graph shifts 2 units downward
(B) Lana’s graph shifts 2 units upward
(C) Lana’s graph shifts 2 units to the left
(D) Lana’s graph shifts 2 units to the left
71. In a classic math problem a king wants to reward a knight who has rescued him from an attack. The king gives the knight a chessboard and plans to place money on each square. He gives the knight two options. Potion 1 is to place a thousand dollars on the first square, two thousand on the second square, three thousand on the third square, and so on. Option 2 is to place one penny on the first square, two pennies on the second, four on the third, and so on.